ecdf {stats}  R Documentation 
Empirical Cumulative Distribution Function
Description
Compute an empirical cumulative distribution function, with several methods for plotting, printing and computing with such an “ecdf” object.
Usage
ecdf(x)
## S3 method for class 'ecdf'
plot(x, ..., ylab="Fn(x)", verticals = FALSE,
col.01line = "gray70", pch = 19)
## S3 method for class 'ecdf'
print(x, digits= getOption("digits")  2, ...)
## S3 method for class 'ecdf'
summary(object, ...)
## S3 method for class 'ecdf'
quantile(x, ...)
Arguments
x , object 
numeric vector of the observations for 
... 
arguments to be passed to subsequent methods, e.g.,

ylab 
label for the yaxis. 
verticals 
see 
col.01line 
numeric or character specifying the color of the
horizontal lines at y = 0 and 1, see 
pch 
plotting character. 
digits 
number of significant digits to use, see

Details
The e.c.d.f. (empirical cumulative distribution function)
F_n
is a step function with jumps i/n
at
observation values, where i
is the number of tied observations
at that value. Missing values are ignored.
For observations
x
= (
x_1,x_2
, ... x_n)
,
F_n
is the fraction of observations less or equal to t
,
i.e.,
F_n(t) = \#\{x_i\le t\}\ / n
= \frac1 n\sum_{i=1}^n \mathbf{1}_{[x_i \le t]}.
The function plot.ecdf
which implements the plot
method for ecdf
objects, is implemented via a call to
plot.stepfun
; see its documentation.
Value
For ecdf
, a function of class "ecdf"
, inheriting from the
"stepfun"
class, and hence inheriting a
knots()
method.
For the summary
method, a summary of the knots of object
with a "header"
attribute.
The quantile(obj, ...)
method computes the same quantiles as
quantile(x, ...)
would where x
is the original sample.
Note
The objects of class "ecdf"
are not intended to be used for
permanent storage and may change structure between versions of R (and
did at R 3.0.0). They can usually be recreated by
eval(attr(old_obj, "call"), environment(old_obj))
since the data used is stored as part of the object's environment.
Author(s)
Martin Maechler; fixes and new features by other Rcore members.
See Also
stepfun
, the more general class of step functions,
approxfun
and splinefun
.
Examples
## Simple didactical ecdf example :
x < rnorm(12)
Fn < ecdf(x)
Fn # a *function*
Fn(x) # returns the percentiles for x
tt < seq(2, 2, by = 0.1)
12 * Fn(tt) # Fn is a 'simple' function {with values k/12}
summary(Fn)
##> see below for graphics
knots(Fn) # the unique data values {12 of them if there were no ties}
y < round(rnorm(12), 1); y[3] < y[1]
Fn12 < ecdf(y)
Fn12
knots(Fn12) # unique values (always less than 12!)
summary(Fn12)
summary.stepfun(Fn12)
## Advanced: What's inside the function closure?
ls(environment(Fn12))
## "f" "method" "na.rm" "nobs" "x" "y" "yleft" "yright"
utils::ls.str(environment(Fn12))
stopifnot(all.equal(quantile(Fn12), quantile(y)))
### Plotting 
require(graphics)
op < par(mfrow = c(3, 1), mgp = c(1.5, 0.8, 0), mar = .1+c(3,3,2,1))
F10 < ecdf(rnorm(10))
summary(F10)
plot(F10)
plot(F10, verticals = TRUE, do.points = FALSE)
plot(Fn12 , lwd = 2) ; mtext("lwd = 2", adj = 1)
xx < unique(sort(c(seq(3, 2, length.out = 201), knots(Fn12))))
lines(xx, Fn12(xx), col = "blue")
abline(v = knots(Fn12), lty = 2, col = "gray70")
plot(xx, Fn12(xx), type = "o", cex = .1) # plot.default {ugly}
plot(Fn12, col.hor = "red", add = TRUE) # plot method
abline(v = knots(Fn12), lty = 2, col = "gray70")
## luxury plot
plot(Fn12, verticals = TRUE, col.points = "blue",
col.hor = "red", col.vert = "bisque")
## this works too (automatic call to ecdf(.)):
plot.ecdf(rnorm(24))
title("via simple plot.ecdf(x)", adj = 1)
par(op)